Reduction of Unbalanced Magnetic Pull in Doubly-Fed Induction Machine

Transcription

1 Reduction of Unbalanced Magnetic Pull in Doubly-Fed Induction Machine By Obaid Aamir Thei ubmitted in fulfilment of the requirement for the degree of Mater of Engineering (Reearch) School of Electrical, Mechanical and Mechatronic Sytem Faculty of Engineering and Information Technology Univerity of Technology Sydney (UTS) January 2016

2 Certificate I, Obaid Aamir, declare that thi thei titled, Reduction of Unbalanced Magnetic Pull in Doubly-Fed Induction Machine, and the work preented in it are my own. I confirm that: Thi work wa done wholly or mainly while in candidature for a reearch degree at thi Univerity. Where any part of thi thei ha been previouly ubmitted for a degree or any other qualification at thi Univerity or any other intitution, thi ha been clearly tated. Where I have conulted the publihed work of other, thi i alway clearly attributed. Where I have quoted from the work of other, the ource i alway given. With the exception of uch quotation, thi thei i entirely my own work. I have acknowledged all main ource of help. Where the thei i baed on work done by myelf jointly with other, I have made clear exactly what wa done by other and what I have contributed myelf. Signed: Date: 2

3 Acknowledgement Firtly, I would like to expre my deepet gratitude to my principle upervior, Aoc. Prof. David Dorrell for hi continuou orientation, motivation, uggetion and encouragement throughout my degree which helped me to undertand and improve my knowledge in thi area of reearch. Without him thi thei would not exit. I would like alo to thank and acknowledge my friend and colleague for their upport, help and making me feel le alone. Alo, I would to take thi opportunity to how my incere grateful to Univerity of Technology, Sydney, School of Electrical, Mechanical and Mechatronic Sytem who alway encouraged me. Lat but not the leat; I would like to expre my incere thank to my family for their Continuing upport, being patient and faith in me throughout the lat two year. Whatever I have accomplihed in my academic life i becaue of my parent upport and bleing. 3

4 Dedication To my parent, The reaon of what I become today. Thank for your wonderful upport. To my iter, You have been my inpiration. 4

5 Abtract Thi thei report on an invetigation into the unbalanced magnetic pull (UMP) in a wound rotor induction machine due to tatic rotor eccentricity. Wound rotor induction machine are commonly ued in wind turbine a doubly-fed induction generator (DFIG). It i important to maintain them in good working order and operational. There can be ubtantial bearing wear in thee machine due to their almot continuou operation, and it i important to maintain low bearing wear of thee machine in order to maintain good operation. Thee machine can have high maintenance cot ince they are located in remote location and in the nacelle of the wind turbine. When the rotor become eccentric (non-centred) bearing wear i increaed and the maintenance requirement increae. It ha been illutrated that the UMP i higher per unit in a wound rotor induction machine compared to the cage induction machine equivalent. In thi tudy, a new meaurement rig i developed in order to meaure UMP. The method for calculating UMP and plitting UMP and torque force are addreed in thi thei. Furthermore, a new method for minimizing UMP i alo introduced by uing damper winding. Different tet and calculation are preented in thi thei. The undertanding of the radial force involved in producing UMP in a wound rotor induction machine i addreed. There i little literature on UMP in a wound rotor induction machine. 5

6 Lit of Symbol b y, t Radial flux denity in air gap at point y and time t [T] b y, t Normal flux denity in air gap at point y and time t [T] n b y, t Tangential flux denity in air gap at point y and time t [T] t b r b c e y, t Rotor lot opening [m] Stator lot opening [m] Number of turn in a coil Air gap electric field at point y and at time t [V/m] e y, t Air gap electric field due to tator current at point y and at time t [V/m] f e f r g Electrical frequency [Hz] Rotor fundamental current frequency [Hz] Mean air gap length when the rotor i concentric [m] gxy (, ) h Effective axial air gap length at point x,y in the air gap [m] Search coil number i r x Rotor current [A] i t Harmonic current [A] j y, t Rotor current denity at point y and at time t [A/m] r j y, t Stator current denity at point y and at time t [A/m] j y, t Current denity at point y and at time t [A/m] k x n k r n k n Invere of average air gap radiu [m] Rotor lot opening factor n th harmonic tator lot opening factor Variation in axial direction n n r r p Synchronou peed [rpm] Mechanical peed [rpm] Number of pole pair Mean air gap radiu [m] Motor lip [p.u.] 6

7 x y x C w D F x F y n J K L N w n N Variation in axial direction when analying linearized machine, horizontal direction when analying force on axial cro ection of machine, or horizontal direction of force in UMP meauring rig [m] Variation in circumferential direction when analying linearized machine, vertical direction when analying force on axial cro ection of machine, or axial direction of force in UMP meauring rig [m] Variation in radial direction when analying linearized machine, or vertical direction of force in UMP meauring rig [m] Number of conductor in the w th lot Difference between centre of rotor and tator [m] Force in x (horizontal) direction in axial cro ection of machine [N] Force in y (vertical) direction in axial cro ection of machine [N] Stator current denity coefficient of n th current harmonic [A/m] Slot opening factor Axial length of the tator [m] Number of lot at which winding i located n th harmonic winding coefficient of tator P Air gap permeance [m -1 ] P m Fundamental pole pair number of machine P Mechanical power [W] mech R r Rotor reitance [Ω] T Mechanical torque [Nm] mech V D Induced Voltage [V] Degree of offet [p.u. of air gap length g] Induced EMF [V] Permeability of free pace Maxwell tre [N/m 2 ] n m Ψ m Ψ r Ψ Mechanical rotational velocity [rad/] Air gap magnetic flux [Wb] Rotor magnetic flux [Wb] Stator magnetic flux [Wb] 7

8 Table of Content Acknowledgment 2 Dedication 3 Abtract 4 Lit of Symbol 5 Lit of Table 9 Lit of Figure 10 Chapter: 1 Introduction Background of the tudy Reearch Problem Objective Organization of the Thei Publication Ariing Directly from the Mater Reearch 16 Chapter 2: Literature Review and Reearch Literature Review Reearch Development 20 Chapter 3: Analyi of Machine Machine Slip Torque Air Gap Length Permeance Unbalanced Magnetic Pull Addition of 2 pole and 6 pole Search Winding UMP Attenuation by Additional Winding 40 Chapter 4: Methodology and Experiment Machine Setting Tranducer Meaurement of UMP Open Circuit Tet 54 8

9 4.3.2 Short Circuit Tet pole and 6-pole Search Winding DC Tet 73 Chapter 5: Concluion and Future Work 74 Bibliography 75 Appendix A - Motor Specification 81 Appendix B - 4 Pole Main Winding 83 Appendix C 2 Pole Search Winding 84 Appendix D 6 Pole Search Winding 85 Appendix E - Power Connection 86 Appendix F Technical Paper Publihed 87 9

10 Lit of Table Table 4.1: Rotor nominally centred. Table 4.2: 20% eccentric poition of rotor. Table 4.3: 30% eccentric poition of the rotor. Table 4.4: NDE moved 40% while DE centred. Table 4.5: DE moved 40% while NDE centred. Table 4.6: Short circuit and open circuit with 6 pole winding. Table 4.7: DE 40% Eccentric Table 4.8: NDE 40% Eccentric. Table 4.9: NDE 20% Eccentric Table 4.10: DE 20% Eccentric Table 4.11: DE 5% Eccentric Table 4.12: NDE 5% Eccentric 10

11 Lit of Figure Figure 3.1: Rig including lip ring and graphite bruhe. Figure 3.2: Magnetic pole ytem generated by current in the tator and rotor winding. Figure 3.3: Equivalent circuit Figure 3.4: Simplified Equivalent circuit Figure 3.5: Rotor and tator poitioning Figure 3.6: DE and NDE Eccentricity Figure 3.7: Poition of coil on tator Figure 3.8: Rotor loop repreentation Figure 3.9: 2 pole and 6 pole earch Winding Figure 4.1: 4 Pole wound rotor induction machine Figure 4.2: DE of the motor Figure 4.3: NDE of the motor Figure 4.4: Tranducer Figure 4.5: Analyer Figure 4.6: Component force Senor Figure 4.6: Senor poition Figure 4.7: 1 t ide of machine Figure 4.8: 2 nd ide of machine Figure 4.9: Tet motor cofiguration Figure 4.10: Open circuit UMP meaurement reult Figure 4.11: Rotor with locking bar Figure 4.12: Short circuit locked rotor UMP meaurement Figure 4.13: Effect of axial variation of eccentricity on the UMP Figure 4.14: NDE moved 40% while DE centred Figure 4.15: NDE moved 40% while DE centred Figure 4.16: Axial variation of eccentricity. Figure 4.17: 2 pole and 6 pole Winding Figure 4.18: 6 Pole reult with open circuit and locked rotor. Figure 4.19: 2 Pole winding tet. 11

12 Figure 4.20: DE 40% Eccentric Figure 4.21: NDE 40% Eccentric Figure 4.22: NDE 20% Eccentric Figure 4.23: DE 20% Eccentric Figure 4.24: DE 5% Eccentric Figure 4.25: NDE 5% Eccentric Figure 4.26: Reult of Different rotor eccentricitie Figure 4.27: Comparion of UMP with different rotor eccentricitie Figure 4.28: Comparion of voltage with different rotor eccentricitie 12

13 Chapter 1: Introduction 1.1. Background of the Study The electrical machine produce both tangential and radial electromagnetic force on the urface of the rotor and tator in the air gap. The rotating torque i produced by tangential electromagnetic force when the rotor of the machine i exactly centred and the net radial electromagnetic force on the rotor i zero. Mot electrical machine work with ome degree of rotor eccentricity ince the axe of the tator and rotor rarely correpond to each other. Thi can be due to wear of bearing, bending in the rotor halt, tolerance in manufacturing and many other manufacturing influence. The imbalance in the electromagnetic force on the tator and the rotor produce a net radial force on the rotor if the tator bore axi doe not match with the axi of the rotor. There will obviouly be an equal and oppoite force on the tator. The electromagnetic force acting on the rotor depend on the degree of movement of the rotor axi away from the tator axi. Thi i called rotor eccentricity. The total force i the um of the force acting on the rotor urface around the air gap and thi varie in an irregular manner when there i a net force. Thi net force pull the rotor even further out of alignment and i known a Unbalanced Magnetic Pull (UMP). Further increae in eccentricity and UMP may caue damage to the machine in motion. Rotor eccentricity i expreed in different way, but uually it i defined in term of either tatic eccentricity or dynamic eccentricity. If the radial motion of eccentric rotor remain tationary with the tator, and the rotor till rotate on it own axi, it i called tatic eccentricity and reult in a teady pull force toward the point of minimum air gap. When the rotor till rotate on tator centre but i not rotating on it own axi thi i aid to be dynamic eccentricity, and reult in the rotating UMP force vector. Static eccentricity can be caued by a mialigned or worn bearing whilt dynamic eccentricity can be caued by a bent haft. Both condition can be caued by general manufacturing and aembly variation and can exit together. Mot tudie that attempt to model thi problem aume that the eccentricity i contant down the axial length of the machine but thi i an approximation to the real ituation and axial variation of eccentricity i invetigated in thi tudy. Normal analyi technique uually ignore the tangential force on the rotor urface and only conider the normal force. The analye then uually aume the normal force i produced only 13

14 by the flux croing the air gap in a radial direction. If a harmonic air gap flux wave technique i ued to analye the UMP then it can be hown that the UMP i produce by two flux wave exiting in the air gap which have pole-pair differing by one. Hence, for a 4-pole machine, a invetigated here, rotor eccentricity produce a 2-pole flux wave and a 6-pole flux wave, and thee to flux wave interact with the 4-pole main flux to produce UMP. Along with UMP in the machine, there are different factor which influence in the mechanical wear and aging in an electrical machine, peed and performance. Rotor eccentricity can produce uneven current ditribution in parallel winding in a machine and thee can lead to localized hot pot in ome coil with winding degradation and failure. In recent year, induction machine have been ued in wind turbine ytem a generator. There are two type of induction machine: (a) quirrel cage induction machine and (b) wound rotor induction machine. Both machine have tator tructure which imilar to alternating current ynchronou generator, and thee conit of a hollow cylinder of laminated heet teel with punched longitudinal lot. A Magneto-Motive Force (MMF) wave i produced in the air gap when a polyphae winding (invariably a 3-phae winding in larger machine) i placed in the lot and connected to a uitable ac upply. A wound rotor induction machine rotor i imilar to that of quirrel cage induction machine. The only difference i that hort circuited quirrel cage winding i replaced by a three phae inulated winding in a imilar manner to the tator. The winding of the rotor i uually wye connected and acceed via external lip ring on the haft. Traditionally, the purpoe of lip ring i to provide external additional reitance to each phae of the rotor to improve the tarting characteritic of the motor. There were alo way to recover the energy diipated in the reitor via cheme called lip-energy recovery cheme. However, the concept of the lip-energy recovery ha now been extended to allow generation at ub-ynchronou peed by injecting power into the rotor at lip frequency via the ring, with the power coming from the grid via back-to-back 3-phae inverter. At uper-ynchronou peed power exit the rotor via the lip ring. In thi way the machine can now be ued a a generator with wide peed range and a partially rated inverter ytem, with mot of the power till flowing from the gridconnected tator winding. Thi had led to a renaiance in the ue of wound rotor induction machine. However, Dorrell [56] did how that wound rotor machine do have higher UMP compared to their cage rotor equivalent and given the remote location of many wind turbine and difficult 14

15 acce to the generator at the top of the turbine tower in a nacelle, it i highly advantageou to be able to calculate the UMP in a machine and alo earch for method to minimize the UMP. Any calculation method need to be validated experimentally. To thi end, the main aim of thi tudy wa to et up a tet bed for the meaurement of UMP in a wound field induction machine and initiate the tudy of the ue of auxiliary winding for reducing UMP Reearch Problem A rotating moment about the axi of the induction machine i created if the rotor of the machine i mechanically centred within the tator and lotting effect are neglected. A net radial force created due to change in poition of the rotor at thi untable point pull the rotor further out of alignment; thi force i known a unbalanced magnetic pull (UMP). Thi thei i aimed at tudying of UMP, and alo the reduction of the UMP, in a wound rotor induction machine. When the rotor poition in a tator i not in centre of the tator bore or there i the preence of ome other aymmetric rotational magnetic flux in the air gap of a machine then there i a caue of UMP in the machine. UMP increae wear on bearing and play a role in hortening the life of a machine, or reducing maintenance period of the machine. In extreme cae it can caue failure. Moreover it alo affect the upport tructure of rotor and tator ince it can alo lead to vibration, epecially when the eccentricity i of the dynamic form where the force vector i rotating. Uually UMP i the effect of rotor eccentricity; either tatic eccentricity and dynamic eccentricity or poibly a function of both. The proce of aembling and manufacturing motor may reult in air gap eccentricity. The manufacturing tolerance of the tator bore and centring of the bearing can caue tatic eccentricity a already tated. The wearing and incorrect poitioning of bearing reult in exceive UMP. When the rotor move it poition from the tator centre but till rotate on tator centre, i.e., it doe not rotate on it own centre, i aid to be dynamic eccentricity. Thee both eccentricitie can exit at the ame time. The normal caue of the dynamic eccentricity i a bent haft, manufacturing tolerance and incorrect manufacturing. Incorrect manufacture i le likely to produce thi ituation. Rotor whirl at a critical peed can alo produce dynamic eccentricity although thi may not be ynchronou with the rotor [68]. The non-centred poition of rotor in a tator or the preence of unymmetrical magnetic flux in the air gap caue unbalanced magnetic pull (UMP) in a machine. Thi affect the motor in term of maintaining good performance and caue bearing wear. 15

16 1.3. Objective Induction machine are widely ued a generator in wind turbine a already dicued. It i important to maintain good operation and low bearing wear of thee machine. The radial force and vibrational behaviour of the rotor reult in unbalanced magnetic pull in the machine and thee are key factor in producing exceive bearing wearing and required increaed maintenance. The main objective of thi reearch i to calculate and meaure the unbalanced magnetic pull in the machine caued by tatic rotor eccentricity (which i probably the mot common form of eccentricity) and to develop method to minimize the UMP. In the cae of tatic eccentricity the radial air gap length i fixed and i caued by the incorrect poitioning of rotor or tator at the time of manufacturing or by the ovality of tator core. The occurrence of tatic eccentricity i becaue of rotor centric axi i diplaced from the tator axi but remain tationary with repect to the tator. The permeance harmonic method i ued to analytically calculate the UMP. Thi reearch put forward the methodology to reduce UMP in machine by introducing damper winding in the machine. Moreover, the method of poitioning rotor in different eccentricitie i alo propoed to oberve the minimization effect of UMP in the machine. The main work in thi thei concern the UMP meaurement rig however analyi i put forward to enable further tudy elewhere and the ue of UMP damper winding are dicued. The machine tudied here require rewinding in order to have damper winding with ufficient MMF to control the UMP and wa thu deemed to be outide the cope of the project in term of experimental tudy. However, pole-pecific earch coil were fitted in order to detect rotor eccentricity and thi i reported on Organization of the Thei Thi thei i tructured a follow: Chapter One: Thi chapter provide an introduction to the reearch and the main objective behind thi reearch. Chapter Two: A literature urvey of UMP in rotating electrical machine i preented. Thi chapter aim to review UMP analyi and meaurement method. 16

17 Chapter Three: An analyi method for calculation of the machine UMP i preented in here. The determination of machine lip, torque, permanence and air gap length i preented in thi chapter. Furthermore, the method of coupling impedance i ued to calculate the UMP uing additional pole winding in the machine. Chapter Four: Thi chapter provide a methodology for the meaurement of the UMP and alo propoed a method for minimizing UMP in a wound rotor induction machine. The reult obtained from the propoed method are dicued here. A tudy for the detection of rotor eccentricity i alo put forward in thi chapter and initial reult are given. Chapter Five: Thi chapter preent a concluion and ummary of the thei and ome potential future work for thi reearch Publication Ariing Directly from the Mater Reearch Thi work ha contributed to three technical paper: 1. D. G. Dorrell, and O. Kayani. "Meaurement and Calculation of Unbalanced Magnetic Pull in Wound Rotor Induction Machine." Tran. on Magnetic, IEEE Vol. 50, no. 11, Nov Abtract: Thi paper addree the meaurement and calculation of unbalanced magnetic pull (UMP) in a wound rotor induction machine. A new rig for meauring UMP i preented. To the author knowledge thi type of rig ha not been teted before. The paper detail the force calculation method and a method for plitting the UMP and torque. Wound rotor induction machine are now popular a generator in wind turbine. It i important to maintain good operation and low bearing wear, and the UMP in thee machine i higher than the cage-rotor equivalent becaue the cage damp the UMP. There i little literature on the UMP in a wound rotor machine. 2. D. G. Dorrell, O. Kayani and A. Salah, The detection and uppreion of Unbalanced Magnetic Pull in Wound Rotor Induction Motor Uing Pole-Specific Search Coil and Auxiliary Winding, to be preented at IEEE ECCE Conference, Montreal, Sept Abtract: In large induction machine (uch a large cage induction motor pump in the petro-chemical indutry and cage or wound-rotor induction generator in wind turbine) reliability and longevity i advantageou. Thi i particularly relevant to wind turbine generator which can be inacceible. There will be ome degree of tolerance and wear that will lead to low-level rotor eccentricity. For a pm-pole pair machine there will be pm±1 pole pair flux wave et up by the eccentricity which will generate unbalanced magnetic pull (UMP), a well a additional higher pace harmonic. Thi paper addree the ue of tator damper winding to reduce the ide-band flux wave and hence attenuate the UMP. Example are put forward in term of a 10 pole cage-rotor machine with tatic or dynamic rotor eccentricity and then extended to ue a 4 pole machine wound-rotor machine. A teted analytical model i developed to include 17

18 thee damper winding and the wound rotor; they are hown to reduce the UMP, particularly in a woundrotor machine. The imulation here are in term of a wound-rotor machine but thi can be extended for DFIG operation. 18

19 Chapter 2: Literature Review and Reearch 2.1. Literature Review The reearch on unbalanced magnetic pull emerged in 1918 through a publication on the work carried out to determine UMP [1]. Roenberg worked on critical induction in machine and tried to invetigate whether it reult in higher unbalanced magnetic pull in machine than any other induction machine [2]. He alo tried to evaluate UMP by calculating the air gap flux imbalance uing B-H curve. Hi paper alo decribe UMP effect a a bai on the critical peed in machine deign. Electromagnetic force due to rotor eccentricity have been extenively tudied uing analytical method. UMP in ynchronou and induction machine due to tatic eccentricity wa tudied analytically by Robinon 1943 [3]. A et of linear equation wa preented to calculate the UMP for eccentricitie up to 10 % of the average air gap length. Crawford put forward the conideration of lot combination, winding, rotor aemblie, critical peed, and vibration problem. The method to calculate the vibratory force and acoutic noie have all been invetigated in relation to air gap eccentricity and unbalanced magnetic pull [4]. A tudy of UMP wa performed on machine having erie winding in condition of light load by Covo [5]. He tried to undertand the fluctuating behaviour of eccentric force on machine and calculated UMP more preciely. In [6], Summer put forward on extenive tudy on 2-pole A.C machine and theorized UMP uing rotating field component. He came up with a theory that twice-line-frequency vibration are produced with tatic eccentricity caued by deformation in motor and twice-running frequency vibration are produced due to imbalance and irregularitie in rotor cauing dynamic UMP. The twice-lip-frequency beat vibration are generated a a reaction of tatic and dynamic eccentricity UMP in thee 2-pole A.C machine. The work wa followed by Robinon [7], who found the exitence of line frequency vibration uing mechanical reonance. Further work wa carried out by Jordan [8] in 1967 and Rai [9] in Evidence of rotor eccentricity cauing noie in a machine wa documented by Ellion and Moore [10]. The UMP can be reduced by the ue of parallel winding and thi wa modelled in [3], [ 11], and [12]. 19

20 The dependence of the machine pole number on the damping of the rotating magnetic field in a rotor cage were oberved by Schuiky [13] in The air gap permeance modulate the MMF wave which conit of inuoidal wave erie and a contant component. Thi work explain the preence of the magnetic field harmonic in a machine. The occurrence of homopolar flux wa identified in two pole motor. Thi flux croe the air gap and return through the bearing, haft and caing [14]. In [15] a tudy did contrat the variation between a two pole machine and a machine with more than two pole and concluded that the two pole motor wa a pecial cae. [16] [18] further tudied two pole induction motor and invetigated UMP and homopolar flux in them. Belman [19] tated that there occur a linkage between homopolar flux and UMP in a machine with tatic eccentricity. Hi work howed that a UMP with twice upply frequency i produced by the generation of homopolar flux. The emiion of acoutic noie a a reult of radial vibrating field theory in a two pole ingle phae induction motor wa tudied by [20]. Thi preented the effect on the vibration and noie caued by tatic and dynamic eccentricitie due to homopolar flux in an induction motor. It wa noticed that a number of low frequency radial force in a motor were caued by homopolar flux. [21] reported on further analyi of the noie and vibration in machine. [22] put forward work on UMP which i applicable to different pole number machine. In 1983 [23], Williamon came up with an analyi technique baed on the tudy of machine uing generalied harmonic analyi [23]. Thi method wa earlier ued to identify rotor cage end-ring, inter-ring and tator winding fault by Williamon and Smith in 1982 [24]. Williamon and Mirzoin in 1985 [25], Williamon and Abdel-Magied in 1987 [26] and Williamon and Adam in 1989 [27] alo ued thi idea in their reearch to identify fault in a motor. Thi method determine of coupling impedence, which link variou circuit with current flowing to any winding with applied voltage in the machine. Swan preented a technique of conformal tranformation to tudy induction motor in 1963 [28]. The method of generalied harmonic analyi along with the method of conformal tranformation were ued on induction motor with parallel tator winding to compute UMP by Dorrell and Smith in 1994 [29]. An approach to the tudy of UMP in a machine uing earlier approache wa preented by Smith and Dorrell in 1996 [30]. The divergence in the direction of UMP from the direction of rotor eccentricity due to parallel tator winding wa noted in their tudie together with the generation of twice upply frequency vibration. 20

21 A model for the magnetic field in the air gap of an electrical machine uing permeance harmonic analyi wa preented by Heller and Joke in 1969 [31]. Further work wa carried out by Vandeuelde and Melkebeet in 1994 [32] to identify the integrated effect of rotor aturation, eccentricity and lotting in the analyi of the magnetic field uing permeance harmonic analyi. A procedure to invetigate the EMF in induction machine with the rotor rotating at variable frequencie uing the permeance harmonic theory wa developed by Früchtenicht et al. in 1982 [33]. Winding variable were utilized to model the winding ditribution in order to calculate the MMF in induction machine by Stavrou and Penmare in 2001 [34]. Berman, 1993 [35], tudied the effect of connection equalization in induction machine tator winding with dynamic and tatic rotor eccentricitie uing permeance harmonic analyi. They propoed an effective method to calculate MMF. To oberve and tudy the current and inductance in a machine, WFA (Winding Function Approach) ha been ued in everal different publication [36]-[39]. WFA wa firt preented and ued in [40]. The linear behaviour with increaing MMF in the motor lot and the effect of rotor bar kewing wa tudied in [41]. He alo invetigated the effect on machine inductance. Further invetigation on machine uing thi approach were developed by [42]. A modified approach wa developed in [42] and named MWFA (Modified Winding Function Approach). Further work wa conducted in [43] to [46]. Uing machine with dynamic eccentricity, another tudy of the MMF in the lot and rotor kew wa publihed in [47]. Baio et al gave a new method for the tudy of machine with dynamic and tatic eccentricity in [48]. UMP wa noted a being linear with rotor eccentricity in witched reluctance machine by Garrigan et al. [49]. However, a reduction in UMP wa alo noted when there wa a reduction in air gap in the aturation region. Thi i becaue when the air gap i mall, the teel aturate, o any additional increae in flux i difficult. Their tudy concluded that the winding, connected in parallel played a vital role in reduction of UMP in the machine. Bruhle permanent magnet motor with levitation force and main winding were invetigated uing rotating field theory by Dorrell et al. (2003) [50]. They put forward a mathematical method to calculate the radial force uing the theory on eccentric permanent magnet rotor. Their reult matched well the imulation reult. A conformal tranformation technique preented by Swann 1963 [28] wa utilized by Li et al. [51] in 2007 for a permanent magnet machine in order to determine the magnetic field in the air gap. 21

22 An increae in the UMP when a cage machine wa loaded from no load wa oberved by Dorrell in 1995, and Dorrell in 1996 [52][53]. The machine ha tatic eccentricity. The calculated and meaured reult matched well. Work wa carried out on UMP reduction by Dorrell 1999 in [54] where the factor of parallel tator, rotor winding connection and variable frequency operation where invetigated. Non uniform eccentricity, where the eccentricity change down the axial length of the machine, wa tudie uning rotating fieldtheory by Dorrell 2000 [55]. An analyi wa developed to calculate UMP uing tator current, rotor current, damper current and flux wave in [56]. A wound rotor model wa developed which included tator damper winding. The aumption wa made that the damper winding had little effect on torque, even when there wa rotor eccentricity. It wa hown that the damper winding had little effect in a cage induction motor but it wa hown that they are more effective in wound rotor induction machine. A number of recent paper, e.g., [57] and [58], addreed UMP but few of them actually meaure UMP. A method for meauring UMP by load cell wa propoed in [59], but it had diadvantage: the amount of eccentricity did not remain contant a force i exerted, and a radial movement in eccentricity wa noticed. A method for meaurement of UMP wa put forward in [60]. Piezoelectric tranducer were ued and the rotor and tator mounted eparately. The tator wa mounted on plate and rotor wa mounted eparately on pedetal. Thi method wa quite effective. A finite element analyi (FEA) wa carried out for induction motor with open circuit and hort circuit tet and reult recorded [61] and thi gave detail of the machine ued here. A new tet rig wa etup to meaure UMP of an induction motor under hort circuit rotor and open circuit rotor [62] and thi tudy i the bai for thi thei. The analytical reult from [61] and [62] were analyed uing condition monitoring method [63], [65]. UMP varie with load and voltage in an induction motor and [66] tudied thi. The method of adding damper winding to machine ha been propoed by different reearcher [56], [67], and [68] Reearch Development The meaurement and calculation of unbalanced magnetic pull in a wound rotor induction machine i till in need of further invetigation; there i till little literature on the topic. There i extenive tudy of the cage induction machine in term of UMP, including experimental meaurement, but there i little reearch on the wound rotor induction machine. Thi 22

23 neceitate the meaurement and development of method for the reduction of UMP in order to maintain it performance ince the maintenance cot of thee machine i relatively high. Harmonic winding analyi together with the air gap permeance harmonic method are ue together here in order to put forward a method for calculating the UMP. Static eccentricity i ued becaue thi i likely to be the mot common form or eccentricity and alo it i more traightforward to put into the experimental rig. Tranducer are ued to meaure force acting between the tator and rotor. They were integrated into the rotor mounting. Moving the tator horizontally, and alo himming vertically allowed the rotor to be centred and the UMP minimized. From here the rotor could be moved to put eccentricity into the machine in a controlled and meaured way. The machine wa a 4-pole machine o that additional 2-pole and 6-pole earch winding were intalled into the machine in pace left by the removal of lot wedge. Thee allowed an eccentricity detection method to be invetigated and they were alo invetigated to ee if they could provide ufficient MMF to control the UMP. The former invetigation proved ucceful with eccentricity eaily detected with the pole-pecific earch coil. The latter invetigation did prove unucceful. 23

24 Chapter 3: Analyi of Machine Induction machine are extenively ued a generator in the wind turbine. Thee machine, when in wound rotor form, operate at peed both above and below the ynchronou peed even when generating. Cage induction machine ue a variable frequency inverter to vary the ynchronou peed o that they can alway operate uper-ynchronou and hence generate. The tator tructure of both type of machine are imilar, uually with ditributed 3-pha winding. When a voltage ource i connected to the winding, a magneto motive force (MMF) wave i produced in the air gap when the current flow. The rotor tructure are alo imilar to each other but the hort circuited quirrel cage winding i replaced by a three phae inulated ditributed winding in wound rotor machine and thi winding i acceed via lip ring. The rotor winding are wye connected and attached to three lip ring. Thee lip ring are further connected to the graphite bruhe to provide acce to rotor winding a hown in Fig In thi ection ome fundamental theory of an induction machine will be put forward in term of defining the lip and developing expreion for the torque from the equivalent circuit. After thi more pecific analyi i developed in relation to machine operation with an eccentric rotor. Rotor Slip-ring Stator Figure 3.1: Rig including lip ring and graphite bruhe. 24

25 3.1. Machine Slip Induction machine operate at a peed lightly lower than ynchronou peed n when operating a a motor and jut above the ynchronou peed when generating. When operating a a DFIG, where voltage are applied to the wound rotor circuit, the machine can operate well below and above the ynchronou peed. It i important to calculate the lip of the induction motor which i defined by n n r p.u. (3.1) n where n i the ynchronou peed and n r i the mechanical peed of the rotor. The ynchronou peed of an induction machine i dependent on the machine pole number and the frequency of the upply to the machine. It can be expreed a: n 60 f e rpm (3.2) p where f e i the electrical frequency of the upply and i the machine pole-pair. For determining frequency of the fundamental rotor frequency fr (the lip frequency) the lip and upply frequency are ued: f r f Hz (3.3) e Thi relationhip how that the rotor frequency a a product of lip and electrical frequency and that the rotor frequency varie with lip with contant upply frequency Torque The DFIG machine i a wound rotor induction machine where both the tator and rotor are upplied eparately. The tator i grid connected and the rotor i connected to an inverter to generate voltage et of different lip frequencie. A rotor magnetic field i etablihed due to rotor current and it react with the tator magnetic field which reult in torque. The torque magnitude i determined by angular diplacement and by the magnitude of the product of both the field. The maximum torque occur when the vector are in quadrature to each other a hown in Fig When a balanced 3-phae ource in fed to the tator winding, tator flux i generated with a contant magnitude and it rotate with a ynchronou peed. In thi tate, with 25

26 a rotor open-circuit, there i a no current flow and there i no production of rotor field r o no torque i produced. When the rotor i hort circuited o that the tator flux induce rotor EMF, or the rotor i connected to a eparate lip-frequency upply, current flow in the rotor and produce rotor magnetic flux tator flux r. Thi flux rotate at the ame mechanical peed of the. The torque produced by interaction of two field i T j in Nm (3.4) r r t Figure 3.2: Magnetic pole ytem generated by current in the tator and rotor winding. Thee flux wave rotate at the ame ynchronou peed with repect to tationary tate. The turning of rotor may be aynchronou but the rotational peed of rotor flux i ame a the rotational peed of tator flux. The mechanical torque i related to the power aborbed by reitance component R 1 r in the per-phae equivalent circuit (Fig. 3.3) and alo, if the machine i a wound rotor machine in a DFIG arrangement, the difference between the actual lip-frequency power from the rotor inverter and the power apparently flowing into the rotor in the equivalent circuit from Vr. When the rotor i horted, the mechanical power i calculated from 2 1- P 3 i R mech r r W (3.5) where R = tator winding reitance 26

27 L = tator leakage reactance R r = rotor winding reitance L r = rotor leakage reactance L m = magnetizing reactance k i the effective tator : rotor turn ratio i the lip of the motor. Figure 3.3: Equivalent circuit Fig. 3.4 how a implified equivalent circuit with winding reitance and leakage inductance neglect and the machine phaor diagram which illutrate that for optimal condition for torque production, the magnetizing flux i normal to the phaor of rotor current and flux. Figure 3.4: Simplified Equivalent circuit Uing the implified circuit in Fig. 3.4 the mechanical torque i expreed uing 27

28 P T (3.6) T P (3.7) T mech / / 2 1 Rr 3 ir m Nm (3.8) where T = motor torque i the mechanical rotational velocity. The mechanical rotational velocity i obtained from m 1 p (3.9) After implification: 1 m rpm (3.10) p Subtituting (3.10) in (3.8), we get: R R 3 p i R T 3 i 3 i mech / / / 2 / / 2 1 r / 2 r r r r r 1 p p Nm (3.11) The tator generated flux i expreed a Li Wb (3.12) m m m Ψ m i R / / v r r Li m m Wb (3.13) Replacing i R / / r r in Eq give T 3pΨ i Nm (3.14) mch e m / r 28

29 The above expreion how that the magnitude of rotor current Ψ m control the torque Tmech if both vector are maintained a in Fig / i r and the generated tator flux To obtain the deired torque in a DFIG the rotor current are regulated in uch a way that it magnitude and the magnitude of tator flux act normal to each other but one i rotated by 180 deg electrical o that the torque i now negative. The generation of tator flux magnitude and the phyical poition of the rotor control the torque in a DFIG Air Gap Length In thi ection a thorough derivation of the expreion for the air gap length i given when the rotor i eccentric. Thi i then inverted to obtain an expreion for the air gap permeance. Thi i done for completene of the analyi. There i an air gap between tator and rotor which play an important role on the performance of the machine. The power factor, magnetiing current, noie, cooling and overload capacity are greatly affected by air gap length. Induction machine are deigned taking into conideration the air gap length for the performance of motor. In order to analye the air gap length in a machine conider the tator and rotor a cylinder a hown in Fig y (x,y) Stator Z R r R x Rotor D Figure 3.5: rotor and tator poitioning The equation of a circle, which can be ued to repreent the rotor which i offet a ditance D from the origin i ( D x) y Rr (3.15) 29

30 D repreent the difference between the tator and rotor centre. Expanding the Eq D Dxx y R (3.16) r Rearranging Eq x y R 2 Dx D (3.17) r According to the Pythagora theorem x y z (3.18) Subtituting Eq in Eq z R 2DxD (3.19) r Since x z co, uing trigonometric equation and ubtituting in Eq we get z 2 Dz co R r D (3.20) By rearranging we get: z 2Dzco D co R D D co (3.21) r r ( zdco ) R D 1 co (3.22) D 2 ( zdco ) Rr co Rr (3.23) D ( z Dco ) R 1 1 co 2 2 r 2 (3.24) Rr 2 D ( zdco ) Rr 1 co2 1 (3.25) 2R 2 Since 1 co 1 co2 1 2 r (3.26) 2 And D R r 30

31 2 D 1 co2 1 1 (3.27) R 2 2 r Therefore zd co Rr zd co Rr (3.28) zr D co (3.29) r The radial ditance between rotor and tator g i aumed to be 2 g zr o that g R Dco R (3.30) r g R R Dco (3.31) r Since D dg (3.32) av Then g g (1 d co ) [m] (3.33) av where, d = degree of rotor offet [p.u.] D = difference between the tator and rotor centre [m] g av = effective air gap length when the rotor i concentric [m] The above expreion repreent the air gap in between tator and rotor of the machine with tatic rotor eccentricity, a hown in Figure 3.3. The air gap length can be calculated uing Eq Thi equation i expreed in axial (x) and circumferential (y) direction. gxy (, ) g 1 d( x) co ky () x [m] (3.34) av In exponential form uing Euler formula for a coine ix ix e e cox (3.35) 2 Eq.3.34 can be expreed a d( ) jky ( x) jky ( x) gx (, y) x gav 1 e e 2 (3.36) 31

32 Figure 3.6: DE and NDE Eccentricity Now a the motor have Drive End (DE) and Non Drive End (NDE) o, gxy (, ) g av dde d xe DE jkyde xe d jkyde NDE d xe NDE jkynde xe jkynde [m] (3.37) Thi ha to be inverted to obtain an expreion for the inverion Permeance The preence of rotor lot, tator lot, eccentricity of, and diymmetric in, tator and rotor, and magnetic aturation reult in pemeance wave of air gap. It i the invere of air gap length. P 1 (3.38) g Eq i ued to determine air gap in between the tator and rotor of the motor, and ubtituting in 3.38, and auming there i axial variation of the tatic eccentricity at each end P 1 1 gxy (, ) g 1 d( x, y)coθ av (3.39) Thi become 32

33 Pxy (, ) 1 1 (, ) DE g av jky dde xe gxy jky DE d x e d x e DE NDE d NDE jkynde x e jkynde (3.40) So that Pxy (, ) 1 1 DE 1 xe jkyde NDE xe gxy (, ) g jky DE av xe xe DE NDE jkynde jkynde [m] (3.41) where DE L 2x L 2x t t ( x) and NDE ( x) 2dDELt 2dNDELt Thi give a general expreion for the air gap eccentricity where it varie at each end. The axial x = 0 poition i aumed to be at the axial centre of the machine Unbalanced Magnetic Pull For determining the UMP, we need to calculate the current in tator and rotor winding. Uing the coupling impedance method (hown later), the air gap flux denity i divided into a harmonic erie of wave rotating with different pole number in either direction. In the harmonic Fourier erie of the urface current ditribution, current and poitioning of the tator and rotor coil are required. Thi erie i baed on both time and pace component. The complex Fourier analyi of the machine i ued to obtain the conductor denity ditribution expreion in term of harmonic erie. Complex Fourier analyi take in account the magnitude and poitioning of the conductor on the urface of tator and rotor. In Fig. 3.7, a linearized machine urface i conidered with x axial direction variation, y i the tangential direction variation and z i the radial direction variation. In thi frame a coil with c turn i located. Fig. 3.7 how the poition of thi ingle coil on the tator. The complex Fourier erie can be expreed a with where n jnky c e n y (3.42) n y1b y2b n c jnky c jnky (3.43) c e. dy e. dy b b y1b y2b 33

34 c = number of coil turn b = lot opening y = variation in tangential direction Figure 3.7: Poition of coil on tator Eq in exponential form i 2 r n c jnky1 jnky2 c e e dy 0. (3.44) b where k n k c c e e 2 r n n jnky jnky2 (3.45) th n harmonic tator lot opening factor which i defined a k n b in nk 2 (3.46) b nk 2 where 1 k r r = average air gap radiu, b = tator lot opening. 34

35 For a et of erie connected coil Eq can be expreed a x n x jnky (3.47) n n y N e where n i the harmonic number = 1, 3, 5, etc. and N n x N 1 n jnky kcwe (3.48) 2π r 1 Cw i the number of conductor in w th lot and n k i the lot opening factor which i cloe to unity and can initially be et to unity. The winding current i defined by j t ix t Re Ixe (3.49) The current denity on urface i therefore j x yt, Re N e n n j t-nky x Ix (3.50) Thi i alo known a the MMF wave on the urface. The tator MMF wave i jy, tre N e n n jtnky I (3.51) The rotor conductor ditribution i alo obtained imilar manner to tator jry, tre N e n n jtnky r Ir (3.52) The rotor with conductor can be repreented imilar to tator a hown in Figure 3.7. The conductor ditribution will be n r y jnky Ne r (3.53) n where N r n jnky ke r (3.54) 2π r and the rotor lot opening factor i 35

36 k n r in( nk) (3.55) nk where l = number of loop. y = tangential direction variation. k = average gap radiu. The flux denity due to current ditribution can be calculated uing Ampere law a, j y t by, t. dy (3.56) g y np m (, ) Re m j t np ky byt B e (3.57) n The electric field can be calculated from db y, t ey, t. dy (3.58) dt Thi i alo known a the air gap EMF wave. When the machine i in the tate of tatic eccentricity in the direction of diplacement the normal tree in the air gap can be expreed by Maxwell tre. n,, 2 bn y t bt y t n (3.59) 2μ 0 where n indicate normal component and t indicate tangential component. The normal component of the flux denity can be obtained from 0 bn y, t jy, t. dyc g ( y) (3.60) where μ0 i the permeance of free pace. At no load the tangential component b, relatively mall compared to b, n y t and i neglected o that t y t i 2 bn y, t n (3.61) 2μ o 36

37 Since the air gap flux denity b, n y t i a function of MMF and total permeance P and i a function of rotor poition with repect to time. Then air gap flux b, μo bny, tμop jxy, tdy jxy, tdy g 1 co So Maxwell tre become av n y t i (3.62) μ 0 jx y, tdy gav 1 co 2 μ o 2 (3.63) Solving Eq further we get 2 μo jx y, t dy 2 g 1 co 2 μ av 2 o (3.64) n μore Nx I xe n 2 1 nkg co av 2 2 j tnky 2 (3.65) Uing the Maxwell tre, the force component in the x and y direction can be calculated from 2 F rl co d (3.66) x 0 x 2 n jtnky μ Re 2 o Nx I xe n co (3.67) nkgav 1 co F rl d and 2 F rl in d (3.68) y 0 y 2 n jtnky μ Re 2 o Nx I xe n in (3.69) nkgav 1 co F rl d 37

38 where r = Mean air gap radiu. L = Axial length of the tator. The equation help in the undertanding and calculation of the UMP in the machine. It can be een in the denominator that there i a (1 δ co ) 2 term inide the integral. Even when worked through it can be een that the UMP i approximately proportional the degree of eccentricity Addition of 2 pole and 6 pole Winding The Machine i modified with the addition of 2 pole and 6 pole winding located in pace at the top of the lot. Thi pace wa obtained by the remove for lot wedge. The machine i old and the winding wa ridged o that thee could be removed. Thi wa done to ae a method for meauring the eccentricity and alo to the UMP in the machine taking axial variation in the eccentricity into account. Thee two pole and ix pole winding are introduced a hown in Fig There wa one 6-pole winding and alo two 2-pole winding in quadrature. The winding diagram of thee 2-pole and 6 pole earch winding are hown in Appendice C and D repectively. The machine pecification i given in Appendix A and the main winding given in Appendix B. Figure 3.9: 2-pole and 6-pole earch winding 38

39 In a machine, a erie of the flux wave contribute to the production of UMP in the motor. For the generation of additional air gap flux wave, permeance modulation due to eccentricity i utilized to produce a rotating electric field in the air gap with the correct pole number to induce voltage in the pole-pecific earch winding. In thi intance, for the 4-pole winding, voltage are induced in the 2-pole and 6-pole earch winding. If the winding with more turn and MMF capacity were ued for the earch coil then they can be hort circuited and the induced voltage generate current. Thi current will et up air gap flux wave too and thee will oppoe the voltage-inducing flux wave, i.e., they will damp the UMP. Thi i imilar the effect of uing parallel winding. For determining additional air gap flux wave in motor the MMF equation (Eq. 3.53) i ued. n j( tnky) j y, t Re N I e (3.70) n where NI J n n Subtituting in Eq n j t nky j y, t Re J e (3.71) n Uing the identity a exp j2 3 for a balanced 3 phae current, then n n n1 1n J N 1 a a I (3.72) n n n n 3 n N n1, 5,7 J N a a I I (3.73) For a machine pole-pair number pm, Eq i modified to n j( tnp ky) (3.74) n m j y, t Re J e Modifying Eq. 3.48, tator winding coefficient of ingle phae winding i obtained N k Nw n w 2 w 1 jn pmkyw k C e (3.75) 39

40 A we know k 1 ubtituting in Eq r N n Nw 1 jnpmkyw kcwe (3.76) 2 r w1 Where p m = pole pair number of the machine N w Number of lot where the winding i located C w Number of conductor in w th lot Uing Eq. 3.46, the lot opening factor k can expreed a k 2in 0.5 np m kb (3.77) np kb m The flux denity in the tator due to current ditribution i calculated uing Ampere law a in Eq Eq i ubtituted in Eq and modified to get the mathematical expreion. b x y t j y t dy (3.78) 0,,, g x, y Ampere circuital law can be applied uing the equation b(, x y,) t o(, x y) j(,) y t dyc (3.79) Thi lead to npm j( tnpmky ) npm1 j( tk ( npm1) y) npm1 j( t k ( npm1) y) (,, ) Re ( ) ( ) n b x y t B e B x e B x e (3.80) Eq expree the air gap flux ditribution and how the additional flux wave where B npm j J n 0 and knp g m av j J ( ) ( ) repreent flux denity magnitude. n npm 1 0 B x x knpmgav In the imilar manner Eq. 3.57, thi can be ued to calculate the EMF in the additional winding. Subtituting Eq in Eq we get the tator EMF: 40

41 db x, y, t e x, y, t dy (3.81) dt jtkpm 1y e x y t E x e (3.82) pm 1,, where B ( x) jj E ( x) ( x) npm 1 n pm kpm 1 k pmpm 1gav (3.83) For obtaining expreion for induced EMF in thee winding, the following expreion are ued which are modified according to each pole pair number which ha two winding in α and β axe quadrature. l 2 2 r p 1 p m m 1 (,, t) Re,, ( ) e 1 x y t h n h 1, y dydx (3.84) l 2 0 l 2 2 r p 1 p 1 (,, ) Re m m t e x, y, t n ( ) h 1 h 1, y dydx (3.85) l 2 0 where p 1 p m m1 j p1 ky ( y) N e h1 h1, (3.86) n n p m1 p m1 j p1 ky ( y) jn e h1 h1, (3.87) p m1 p m1 j p1 ky ( y) h1 h1 n N e, (3.88) and p m1 p m1 j p1 ky ( y) h1 h1 n jn e (3.89) N pm 1 where h 1 i defined uing Eq Nw p m jn p ky m w N k h 1 Cwh 1e (3.90) 2r 1 And N p m 1 1 N k C e jnp 1ky m (3.91) h1 h1 2r 1 where h = earch coil number 41

42 Ignoring the winding harmonic in the motor, o with n =1, air gap flux i repreented a follow uing Eq b( xyt,, ) B e B ( xe ) B ( xe ) (3.92) pm j( tpmky) pm1 j( 1tk( pm1) y) pm1 j( 2tk( pm1) y) For the DE and NDE of the machine a hown in Fig. 2.5, NDE in order to calculate the UMP from Eq.3.60 o that B ( np m 1) ( x) i applied to both DE and b x, y, t p ( ) 1 ( 1 ( 1) ) 1 ( 2 ( 1) ) 2 m j tp m ky p m j tk p ( ) m y p m j tk p ( ) m y B e B x e B x e (3.93) 2 And Force for x and y component i calculated by 0 F x 2 Fx rlco d 0 ( ) 1 ( 1 ( 1) ) 1 ( 2 ( 1) ) 2 2 pm j tpmky pm j tk pm y pm j tk pm y B e B ( x) e B ( x) e rlcod (3.94) Fy rlind 0 ( ) 1 ( 1 ( 1) ) 1 ( 2 ( 1) ) 2 2 pm j t pmky pm j t k pm y pm j t k pm y B e B ( x) e B ( x) e Fy rlin d (3.95) UMP Attenuation by Additional Winding 0 The main purpoe of thi tet i to meaure the attenuation on UMP caued by the MMF in the earch winding which can be utilized a damper winding if they have ufficient turn and MMF capacity. They are hort circuited or even additional voltage can be injected. The ue of thee damper winding ha been ued elewhere. In term of condition monitoring of the open circuit earch coil winding (voltage), or hort circuit damper winding (current), it doe appear to be a traight forward method of detecting machine functional fault and the maintenance 42

43 cot are reduced due to at early tage detection. Thi help in minimizing the chance of motor failure in plant. In the pat extenive work wa carried out for the detection of fault uing condition monitoring. Hwang et al. [69] mentioned flux monitoring a an accurate and reliable technique for acquiring information on the electrical machine condition. A et of equation i put forward in [70], [71] that inpect the relationhip between the air gap flux, tator current, air gap eccentricity and vibration ignal. Search coil were included at the rear of the machine to determine the eccentricity and rotor bar fault on the bai of meaurement of leakage flux in [72]. The main purpoe of uing the leakage flux meaurement i it eae of implementation. In [73], Verma et al. preented work and tated that the change of the air gap flux denity i a function of tatic eccentricity. The utilization of pecial flux enor for condition monitoring of electrical drive wa preented by Froini et al. [74]. Placement of earch coil under the wedge of tator winding of a motor i done in order to meaure the actual magnetic flux wa ued in [75]. The ame methodology of placing earch coil under the wedge of tator winding in a machine i ued in our experiment to detect the winding voltage. For thi purpoe the development of an independence matrix i required. V Zi (3.96) Where V i the induced voltage, Z a an impedance and I i the induced current in the winding. In order to implify the analyi then the machine i aumed to have an open circuit rotor and running light. Eq (3.96) can be written in the form of matrix a: v ph i ph vpm1 0 vpm1 Z0 v 0 pm1 0 v pm1 (3.97) 43

44 v ph Z, 0000 ph ph i ph vpm1 Zpm1, ph vpm1 Zpm1, ph v 0 pm1 Zpm 1, ph v pm1 Zpm 1, ph 0000 (3.98) where Zph, ph Rph jxleakage jxmag (3.99) and jxmag can be abtracted from the following implification uing the expreion for EMF: l 2 2 r p m () x, y, t n ( y) dydx (3.100) p m t Re e h l 2 pm m where,, 0 P jtkpm y e x y t E x e (3.101) E B ( x) jj, (3.102) npm n pm 0 ( x) 2 2 kpm k pmgav n y N e (3.103) pm pm jpmky and J n n 3N I (3.104) n1, 5,7 It i relatively traightforward to extend the analyi to include the rotor current, and thi will be the focu of future work. Subtitute Eq. (3.104) in Eq. (3.102), Eq. (3.102) in Eq. (3.101), and Eq. (3.101) and Eq. (3.103) into Eq. (3.104). After implification we obtain: j t t Re jx I e (3.105) h And the value of * 0LN t t X 3 2 Nt (3.106) k p g m av 44

45 which i Xmag and i known a the magnetizing reactance. The other two factor: tooth MMF and core back MMF in Eq. (3.99), can be neglected depending on the deign and manufacture of the machine. In a imilar manner the expreion for other impedance are obtained from 3 LN Z j N 1 * 0 p 1 1, (mean) m pm ph 3 h1 k pmpm 1gav 3 LN Z j jn 1 * 0 p 1 1, (mean) m pm ph 3 h1 k pmpm 1gav 3 LN Z j N 1 * 0 p 1 1, (mean) m pm ph 3 h1 k pmpm 1gav 3 LN Z j jn 1 * 0 p 1 1, (mean) m pm ph 3 h1 k pmpm 1gav (3.107) (3.108) (3.109) (3.110) For control of UMP additional winding current are introduced into Eq. (3.98), then v Z Z Z Z Z ph i 0 Z Z i 0 Z 0 Z 0 0 i 0 Z 0 0 Z 0 i 0 Z Z i ph, ph ph, pm1 ph, pm1 ph, pm1 ph, pm1 ph pm1, ph pm1, ph pm1 pm1, ph pm1, ph pm1 pm1, ph pm1, ph pm1 pm1, ph pm1, ph pm1 (3.111) If the winding are hortened then LN Z j N 1 0 p 1, 1 (mean) m ph pm 3 h1 k pmpm 1gav LN Z j jn 1 0 p 1, 1 (mean) m ph pm 3 h1 k pmpm 1gav LN Z j N 1 0 p 1, 1 (mean) m ph pm 3 h1 k pmpm 1gav LN Z j jn 1 0 p 1, 1 (mean) m ph pm 3 h1 k pmpm 1gav (3.112) (3.113) (3.114) (3.115) UMP can alo be obtained in the imilar manner a expreed 45

46 i ph i pm1 F F, ph F, pm 1 F, pm 1 F, pm 1 F, pm1 ipm 1 F F, ph F, pm1 F, pm1 F, pm1 F, pm1 ipm 1 i pm1 (3.116) Thi outline the method that can be ued to damp and control the UMP through axillary winding. The pecific earch winding fitted to the machine have too few turn and are of thin wire o that the MMF i inufficient to affect the UMP. Thi wa teted by injection of DC current into both the main winding (5 A) and earch coil (0.5 A). There wa no detectable change in UMP. However, there wa good EMF induced into thee winding when the rotor wa eccentric and thi i tudied later in the next chapter. 46

47 Chapter 4: Methodology and Experiment 4.1. Machine and Setting For calculating the UMP, a new tet rig i developed. A 4-pole wound rotor induction machine wa utilized for thi purpoe. Thee machine are commonly ued in wind turbine ytem a generator. Thi machine i alo known a Doubly Fed Induction Generator (DFIG) a both tator and rotor are eparately connected to power upplie. The inulated winding of rotor of thi machine i connected to external lip ring on the haft via a WYE connection. The main pecification in given in Appendix A and the winding diagram i hown in Appendix B The main purpoe of the lip ring i to provide reitance to rotor winding in erie on tarting for thi particular machine. The main purpoe of thi reitance i to reduce tarting current and increae torque in the tate of rotor ince it i a motor. The tet rig i hown in Fig Slip-ring Rotor Metal plate Stator Tranducer Figure 4.1: 4 Pole wound rotor induction machine 47

48 The machine rotor wa et on a pair of metal plate and bolted tightly with the bae to reduce the vibration due to the motion of rotor. Thee metal plate upport the rotor bearing of the Non Drive End (NDE) and drive End (DE). Within thee rotor upport tructure are the piezoelectric force tranducer which meaure the UMP force. The machine upport are hown in Fig. 4.2 and 4.3. Metal plate Tranducer Figure 4.2: NDE of the motor 48

49 Metal plate Tranducer Figure 4.3: DE of the motor The rotor of the motor i eparately mounted on the plate which are helpful in poitioning of the rotor and etting of air gap between rotor and tator during the experiment. Thi i hown clearly in Fig. 4.2 and 4.3. A et of two tranducer are mounted at each end of the rotor mounting on top of the metal plate a hown in Fig Thee tranducer are ued to meaure the UMP and there are four of thee in total. Figure 4.4: Tranducer 49

50 Figure 4.5: Analyer The radial force that are generated are due to the UMP of the motor. For diplaying the meaured force thee tranducer are connected to digital analyer, a hown in Figure 4.5. For meauring the height and the air gap between the rotor and tator, clock gauge are ued for thi purpoe. The parameter of the motor are given in the Appendix A Tranducer Tranducer are ued to meaure the active force regardle of point of action. A et of 4 enor are ued to meaure force in the experiment and each tranducer conit of a 3-component force enor which meaure the force introduced through the top plate. A pair of 3 quartz plate i ued to meaure the force in the x, y and z direction. In each enor, poitive and negative charge appear at the connection depending upon the direction of force applied. Poitive charge give negative voltage at the output of the charge amplifie and vice vera. Fig. 4.6 how 3 component force enor in each of the enor. 50

51 Quartz Plate X Quartz Plate Z Poitive and Negative charge Quatrz Plate Force Quartz Plate Y Figure 4.6: Component force Senor Thee enor are connected to a umming box through integrated 3 wire cable. They are mounted under the metal plate on which the motor i mounted. Fig. 4.6 how the placement of enor on the tet bed. The umming box i connected to a multichannel change amplifier for meauring multicomponent force. It work on piezoelectric meaurement concept, where enor covert mechanical quantitie into an electric charge. From the Fig. 4.7, it can be een that the enor are placed in parallel to meaure the entire acting force. 51

52 Figure 4.7: Senor poition The eight channel charge amplifier calculate the force on each channel a follow Channel 1 = Fx1+2 (4.1) Channel 2 = Fx3+4 (4.2) Channel 3 = Fy1+4 (4.3) Channel 4 = Fy2+3 (4.4) Channel 5 = Fz1 (4.5) Channel 6 = Fz2 (4.6) Channel 7 = Fz3 (4.7) Channel 8 = Fz4 (4.8) To formulate calculation following expreion are ued: Fx = Fx1+2 + Fx3+4 (4.9) Fy = Fy1+4 + Fx2+3 (4.10) Fz = Fz1 + Fz2 + Fz3 + Fz4 (4.11) The experimental work i carried out to determine UMP in the machine and to reduce the UMP uing different technique of moving rotor eccentricity by changing rotor eccentricity in the DE and NDE. Only the x and z component are needed ince the z meaure the axial thrut. 52

53 4.3. Meaurement of UMP A 4 pole wound rotor induction machine i utilized to perform the experiment. Thi machine i et on a pair of metal plate and i bolted tightly with the plate bolted with the bae; the reaon of bolting it tightly with the bae i to reduce vibration in the machine in running condition. Thee both plate are et on the ide of the machine a hown in Fig. 4.7 and 4.8. Figure 4.7: 1 t ide of machine. 53

54 Figure 4.8: 2 nd ide of machine. The rotor of the machine i eparately mounted on plate, which help in adjuting the height of the rotor with repect to the tator. Thi i dine uing him. The end of the machine with lipring and carbon bruhe i named a Non-Drive End (NDE) and the end with machine with the drive haft i named a Drive End (DE). The piezoelectric tranducer are et under the metal plate mounting rotor on DE and NDE, a hown in Fig The machine i then excited and the connection of machine with an autotranformer a hown in Appendix E. Thee tranducer are ued to meaure UMP force acting on the machine in the running tate and are capable of meauring force in the x, y and z direction. The force are meaured a follow Fx12, Fz1 and Fz2 for the DE and Fx34, Fz3 and Fz4 for the NDE. There are 3 channel for each end. Defining the ditance between the vertice of the haft axi to the centre of tranducer a x and the length of the haft axi from the height of tranducer a y a hown in Fig

55 Shaft Metal Plate Then the vertical force can be defined a: Figure 4.9: Tet motor cofiguration F F F F F (4.12) zt z1 z2 z3 z4 Conidering the point of meeting where vertice from the haft meet the horizontal line between the tranducer, we can equate x and z in order to calculate the net x direction force: F F F (4.13) xt x1 x2 Since the z direction force are tangential to x direction force, then F xt tan F (4.14) z From Fig. 4.9 it can be een that. So Eq become (4.15) 55

56 FxT x Fz 1Fz 2 Fz 3 F y z4 (4.16) The open circuit (running light tet) and hort circuit (locked rotor tet) are performed to meaure UMP of the machine. Under load condition (locked rotor) UMP and torque exit together at the ame time and can be eparated depending on locking bar whether it i blocked againt the rotor mounting and tator bed. The torque expreion i T Fdin (4.17) T F in F in F F co F F co (4.18) x1 x2 z1 z2 z4 z3 While running a torque tranducer can be ued to eparate torque and UMP in the machine. The normal air gap in an induction motor i uually mall which make it difficult to et and meaure eccentricity. The rotor and tator of the machine were not at the ame height. In order to bring rotor and tator height into alignment, the rotor mounting were himmed with thin metal plate. Thee him plate were meaured to be 0.35 mm uing Vernier calliper. Adjuting the height of the rotor alo et the air gap between rotor and tator. The air gap between the tator and rotor wa meaured uing clock gauge. Thi i a trial and error method ued after the rotor wa nominally centred. Thi wa done my minimizing the UMP of the machine. The air gap wa continuouly meaured uing clock gauge. When etting the centre poiton, a number of trial fitting wa done until it wa nominally centred with an air gap length of 0.55 mm. The motor i teted under open circuit tet and hort circuit tet to obtain the UMP Open Circuit Tet The rotor of the motor i mounted on the haft and the centre line of the haft doe not coincide with the centre of the ma. A centrifugal force i produced when the haft rotate and thi force bend the haft toward the centre of eccentricity of the ma. Thi caue the initial eccentricity of the rotor in a machine. The rotor wa nominally centred with a 0.55mm air gap. By the help of him to level the rotor, it wa found that the rotor had 4% (0.04 x 0.55 = 0.022mm) eccentric at the tart of the tet which make rotor centred with 0.57 mm air gap. The machine wa then excited and force are tabulated in Table 4.1. The force wa meaured 56

57 at different voltage from 0 to 240V uing an autotranformer. The rotor wa open-circuit and thi i effectively equivalent to the running light tet in a cage induction motor. Table 4.1: Rotor nominally centred. V I FX12 FX34 FY14 FY23 FZ1 FZ2 FZ3 FZ4 εfz The rotor wa then moved from 4 % eccentricity to 20 % eccentric poition (nominal); the eccentricity wa found to be 14 %. The force were again tabulated with voltage variation a hown in Table 4.2. Table 4.2: 20 % eccentric poition of rotor. V I FX12 FX34 FY14 FY23 FZ1 FZ2 FZ3 FZ4 εfz

58 Now the rotor i moved to the 40 % eccentricity poition and it wa found to be 30% eccentric. The reult are tabulated in Table 4.3. Table 4.3: 30 % eccentric poition of the rotor. V I FX12 FX34 FY14 FY23 FZ1 FZ2 FZ3 Fz4 εfz Thee meaured force were then matched with the reult obtained uing Finite Element Analyi (FEA). Thi wa done to adjut the poition from the approximate nominal poition et with the clock gauge. It wa found that meaured UMP wa nearly matched with the FEA reult a hown in Figure

59 UMP [N] Nomonal centered meaured (-4 % etimated) Nominal 20 % Ecc. meaured (14 % etimated) Nominal 40 % Ecc. meaured (30 % etimated) FEA imulated centered FEA imulated 20 % FEAimulated 30 % FEA imulated 40 % Analytical im. 30 % Line voltage [V] Figure 4.10: Open circuit UMP meaurement reult. Thee reult how that an increae in UMP occur a voltage increae. Thi i verified with the theory of the machine when voltage i applied to the rotor diplacement it give rie to UMP. However, a the voltage approache the rated value of the machine then it level out a the core tart to aturate Short Circuit Tet: The rotor bar i locked uing a locking bar a hown in Figure 4.11 to perform the experiment. 59

60 Figure 4.11: rotor with locking bar. The machine wa then excited and everal reult were obtained when rotor wa hort circuited at the lip ring. Thee meaured reult again matched well the imulated analytical reult. For the kewed analytical imulation, the meaured UMP i ignificantly higher than the unkewed imulation at all eccentricitie. The kew increae the UMP a dicued in [64]. There i an axial aturation and damping effect on UMP due to the kew on the rotor. The flux level will change along the axial length ince the phae angle between the tator and rotor flux wave will vary down the axial length of the machine [66]. 60

61 UMP [N] FEA Simulated unkewed rotor Meaured- kewed rotor Analytical kewed Rotor Eccentricity [% of airgap length] Figure 4.12: Short circuit locked rotor UMP meaurement. When the machine wa teted rotor with a locking bar, torque wa obtained by meaurement. Torque wa extracted from the force meaurement when rotor wa locked with a locking bar againt the tator bed. The tet wa performed with Vph = 48 V and line current Iline = 11.1 A and A imulated. The torque wa 5.1 Nm meaured and 4 Nm imulated. It wa found that the correlation reaonable for a locked rotor tet. Thi torque can be difficult to predict and the difference i probably partly due to the kew which increae the effective rotor reitance. The tet were alo performed with changing rotor poition at the DE and NDE. Firt the rotor poition wa changed at the DE to 40 % eccentricity with the NDE kept at nominally centred eccentricity. It wa repeated again with the NDE poition changed to 40 % eccentricity and the DE kept nominally centred. It wa found the changed poition end had higher force acting on it in both cae a hown in Figure The net force on the rotor in thi tet i no longer at the axial centre a one end of the rotor i not centred. The end with eccentricity will experience more force than the end which i centred poitioned. Thi wa alo performed with open circuit light running tet and the reult are hown in Figure

62 Figure 4.13: Effect of axial variation of eccentricity on the UMP. Table 4.4: NDE moved 40 % while DE centred. V I FX12 FX34 FY14 FY23 FZ1 FZ2 FZ3 FZ4 εfz Table 4.5: DE moved 40 % while NDE centred. V I FX12 FX34 FY14 FY23 FZ1 FZ2 FZ3 FZ4 εfz

63 Figure 4.14: NDE moved 40% while DE centred. Figure 4.15: DE moved 40% while NDE centred. Figure 4.16: Axial variation of eccentricity. 63

64 From the reult it i clear that a the voltage keep on increaing, the UMP alo increae. Although a linear behaviour i een in the UMP when the DE i centred and the NDE i eccentric, and when the NDE i centred and the DE i eccentric Pole and 6 Pole Search Winding The motor wa modified with different type of earch coil. It wa modified with 6-pole and 2- pole pecific earch winding a hown in Fig Figure 4.17: 2 pole and 6 pole Winding The rotor of the machine wa refitted a previouly and mounted on pedetal that include piezo-electric force tranducer to meaure direct UMP on each bearing. The motor wa teted again with open circuit, and rotor hort circuit with locked rotor. Initially only the 6-pole earch winding (a hown in Appendix D) wa implemented and teted. The motor wa then teted with varying eccentricitie (40 %, 60 % and 5 %) and the voltage in the 6 pole winding wa meaured. Table 4.6 preent the reult that were obtained from the open circuit and hort circuit tet. 64

65 Table 4.6: Short circuit and open circuit with 6 pole winding. Centred 0.55 mm airgap Short Circuit (50V, 4.2 A) 6-pole V FX12 FX34 FY14 FY23 FZ1 FZ2 FZ3 FZ4 Read 1 456mV Read 2 456mV Open Circuit (200V, 0.93 A) 6-pole V FX12 FX34 FY14 FY23 FZ1 FZ2 FZ3 FZ4 Read 1 1.6V Read 2 1.6V At 0.4 mm min airgap eccentricity (40 %) Short Circuit (50V, 4 A) 6-pole V FX12 FX34 FY14 FY23 FZ1 FZ2 FZ3 FZ4 Read 1 576mV Read 2 568mV Open Circuit (200V,0.91 A) 6-pole V FX12 FX34 FY14 FY23 FZ1 FZ2 FZ3 FZ4 Read V Read V At 0.2 mm min air gap eccentricity (60 %) Short Circuit (50V, 4 A) 6-pole V FX12 FX34 FY14 FY23 FZ1 FZ2 FZ3 FZ4 Read V Read V Open Circuit (200V, 0.78 A) 6-pole V FX12 FX34 FY14 FY23 FZ1 FZ2 FZ3 FZ4 Read V Read V The Figure 4.18 how the characteritic of the UMP a it varie with eccentricity. There i a degree of eccentricity variation down the axial length of machine and the degree of eccentricity i not precie. 65

66 Figure 4.18: 6 pole reult with open circuit and locked rotor. For further experiment, the machine wa dimantled and 2-pole earch winding were inerted (a hown in Appendix C) on quadrature axe (α and β). The reult how linear characteritic. The eccentricity wa le in thi tet. The hort circuit tet wa done at 50 V and if linearity i aumed, then thee reult hould be four time le but the induction motor demagnetize a it i loaded and reult in UMP. The open circuit tet voltage for the 2-pole winding are hown in Fig It can been een that it ha a linear characteritic. The voltage for 2-pole winding are higher. The 2 pole voltage hould be caled by 3/2 with repect to the 6-pole voltage when conidering the number of earch winding turn and the analyi in the previou chapter. Thi approximately hold. The voltage in the 2-pole winding were invetigated and found to be 90 degree out of phae. Thi i expected. 66

67 Figure 4.19: 2 pole winding tet. The reult in Table 4.7 to 4.12 how reult from non-uniform eccentricity in the machine. The tet tarted with 40 % eccentricity at one end and the rotor i then moved one end at time to reduce the eccentricity. A average eccentricity i reduced, the UMP and earch coil voltage are alo reduced. Thi illutrate that even with non-contant eccentricity, the earch coil detection method can be ued to predict eccentricity. The earch coil were open circuit and the voltage meaured. They were alo horted and a current wa induced into them. Fig 4.26 give the raw UMP data for farce ate each end of the machine. From the comparion between UMP with different rotor eccentricitie in Fig it i clearly noticed that the UMP of the machine reduce with the rotor eccentricity pattern that i followed. Thi evaluate that eccentricity play a vital role in the reduction of UMP in the machine. Similarly Fig i a comparion between the voltage of the earch coil winding and the UMP of the machine. When following the ame pattern of the rotor eccentricitie, the reult are in a decending order of voltage in the earch coil winding. 67

68 Thee reult provide evidence for the relationhip between the UMP with the voltage in the earch coil winding. The UMP in the machine decreae with the fall in the voltage of the earch coil winding with the changing eccentricitie in the rotor. Figure 4.20: DE 40 % Eccentric Table 4.7: DE 40 % Eccentric Short Circuit (50 V, 3.5 A) Read 1 2-pole V2 2-pole V1 6-pole V FX12 FX34 FY14 FY23 FZ1 FZ2 FZ3 FZ4 1.8mV 1.3V 880mV ( A2 = 14 ma, A1 = 11 ma) Read 2 after hort circuited 2-pole winding, and the Ammeter reading 23 ma Read 3 after horting 2-pole winding at V, 9.5 A with current 74 ma (A2=45 ma, A1=51 ma) Read 1 2-pole V2 2-pole V1 6-pole V Open Circuit (200 V, A) FX12 FX34 FY14 FY23 FZ1 FZ2 FZ3 FZ4 4.6V 5.6V 5V Read 2 after hort circuited 2-pole winding, and the Ammeter reading 82 ma ( A2=42 ma, A1=37 ma)

69 Figure 4.21: NDE 40 % Eccentric Table 4.8: NDE 40 % Eccentric. Read 1 2-pole V2 680 mv 2-pole V1 6-pole V Short Circuit (50 V, 3.5 A) FX12 FX34 FY14 FY23 FZ1 FZ2 FZ3 FZ4 1.16V 1.12V ( A2= 4 ma, A1= 16 ma) Read 2 after hort circuited 2-pole winding, and the Ammeter reading 14 ma Read 3 after horting 2-pole winding at 124 V, 9.91 A with current 35 ma (A2=32 ma, A1=14 ma) Read 1 2-pole V2 2-pole V1 6-pole V Open Circuit (200 V, A) FX12 FX34 FY14 FY23 FZ1 FZ2 FZ3 FZ4 3.52V 5.2V 4.4V Read 2 after hort circuited 2-pole winding, and the Ammeter reading 85 ma ( A2=63 ma, A1=52 ma)

70 Figure 4.22: NDE 20 % Eccentric Table 4.9: NDE 20 % Eccentric. Short Circuit (50 V,3.51 A) Read 1 2-pole V2 2-pole V1 6-pole V FX12 FX34 FY14 FY23 FZ1 FZ2 FZ3 FZ4 780mV 540mV 480 mv ( A2= 7 ma, A1= 3 ma) Read 2 after hort circuited 2-pole winding, and the Ammeter reading 10 ma Read 3 after horting 2-pole winding at V, 9.62 A with current 35 ma (A2=23 ma, A1=9 ma) Read 1 2-pole V2 2-pole V1 6-pole V Open Circuit (200 V,0.92 A) FX12 FX34 FY14 FY23 FZ1 FZ2 FZ3 FZ4 1.44V 1.44V 1.2V Read 2 after hort circuited 2-pole winding, and the Ammeter reading 14 ma ( A2=14 ma, A1=10 ma)

71 Figure 4.23: DE 20 % Eccentric Table 4.10: DE 20 % Eccentric. Short Circuit (50 V, 3.52 A) 2-pole V2 2-pole V1 6-pole V FX1 2 FX34 FY14 FY23 FZ1 FZ2 FZ3 FZ4 Read m V 720m V 312mV ( A2= 5 ma, A1= 3 ma) Read 2 after hort circuited 2-pole winding, and the Ammeter reading 10 ma Read 3 after horting 2 pole winding at 123 V, 9.7 A with current 39 ma (A2=20 ma, A1=15 ma) Open Circuit (200 V, 0.92 A) Read 1 2-pole V2 2-pole V1 6-pole V FX1 2 FX34 FY14 FY23 FZ1 FZ2 FZ3 FZ4 1.56V 1.12V 1.1V Read 2 after hort circuited 2-pole winding, and the Ammeter reading 22 ma ( A2=16 ma, A1=9 ma)

72 Figure 4.24: DE 5 % Eccentric Table 4.11: DE 5 % Eccentric. Short Circuit (50 V, 3.51 A) 2-pole V2 2-pole V1 6-pole V FX1 2 FX34 FY14 FY23 FZ1 FZ2 FZ3 FZ4 Read 1 960m V 500m V 624mV ( A2= 5 ma, A1= 2 ma) Read 2 after hort circuited 2 pole winding, and the Ammeter reading 8 ma Read 3 after horting 2 pole winding at V,9.55A with current 24 ma (A2=25 ma, A1=9 ma) Open Circuit (200 V, A) 2-pole V2 2-pole V1 6-pole V FX1 2 FX34 FY14 FY23 FZ1 FZ2 FZ3 FZ4 Read 1.84V 2.16V 2V Read 2 after hort circuited 2 pole winding, and the Ammeter reading 32 ma ( A2=19 ma, A1=21 ma)

73 Figure 4.25: NDE 5 % Eccentric Table 4.12: NDE 5 % Eccentric. Short Circuit (50 V, 3.52 A) Read 1 2-pole V2 2-pole V1 6-pole V FX12 FX34 FY14 FY23 FZ1 FZ2 FZ3 FZ4 760mV 700mV 384mV ( A2= 7mA, A1= 2mA) Read 2 after hort circuited 2 pole winding, and the Ammeter reading 7mA Read 3 after horting 2 pole winding at V, 9.7 A with current 52 ma (A2=32 ma, A1=20 ma) 2-pole V2 2-pole V1 6-pole V Open Circuit (200 V, A) FX12 FX34 FY14 FY23 FZ1 FZ2 FZ3 FZ4 Read 1.36V 760mV 760mV Read 2 after hort circuited 2 pole winding, and the Ammeter reading 18 ma (A2=13 ma, A1=8 ma)

74 Figure 4.26: Reult of Different rotor eccentricitie a the rotor i moved. 74